Thursday, December 19, 2013

Risk premia or behavioral craziness?

Cochrane wishes Shiller would give a more rigorous definition of "bubble" (I couldn't agree more), and he also thinks that Shiller is trying to make finance less quantitative and more literary (I somehow doubt this, given that Shiller is first and foremost an econometrician, and not that literary of a guy).

But the most interesting criticism is about Shiller's interpretation of his own work. Shiller showed that, over long time horizons, stock prices mean-revert. He interprets this as meaning that the market is inefficient and irrational - in other words, he attributes mean reversion to what I call "behavioral craziness". But others - such as Gene Fama - interpret long-run predictability as being due to predictable, slow swings in risk premia.

Who is right? As Cochrane astutely notes, we can't tell who is right just by looking at the markets themselves. We have to have some other kind of corroborating evidence. If it's behavioral craziness, then we should be able to observe evidence of the craziness elsewhere in the world. If it's predictably varying risk premia, then we should be able to measure risk premia using some independent data source. Simply appealing to plausibility - i.e., throwing up your hands and saying "Oh, come on!" - is not good enough to resolve the puzzle.

Personally I suspect that it's behavioral craziness, given the fact that experimental asset markets exhibit highly predictable and significant craziness that looks suspiciously like real-world "bubble" episodes. But six undergrads trading tens of dollars in a computer lab is hardly a perfect proxy for the U.S. stock market, so the experimental evidence is suggestive rather than decisive.

There have been some models that have tried to explain how there could be slow, predictable variations in risk premia. The ones I've seen are DSGE-type models that typically involve either consumption habit formation, or Kreps-Porteus preferences (if you don't know what those are, don't ask). Some people swear that the latest of these models have resolved the puzzle. Cochrane is not so sure about the habit-formation models, a sentiment shared by many finance profs I've talked to. (Also, the models of this type that I've seen tend to use RBC-style productivity shocks as the source of aggregate uncertainty, making me pretty skeptical of them right off the bat...but that's just me.)

As for direct evidence of real-world behavioral craziness, this has been scarce...until recently, perhaps. Check out this paper by Robin Greenwood and Andrei Shleifer. They collate six different data sets that ask investors about their expectations of stock returns. The six series are highly correlated, meaning that they are really capturing some general phenomenon in the market. The stated expectations all seem to be "extrapolative", meaning that when returns have been good recently, people think they will continue to be good. But the stated expectations are usually wrong; when people think returns will be high, returns tend to fall soon after. What's more, that fall could be predicted by a simple asset pricing model. In other words, these stated expectations are not rational expectations.

So if these stated expectations really do represent investors' beliefs, then we have direct evidence of behavioral craziness. Now, Cochrane has suggested that people responding to these surveys are not reporting their true beliefs, but rather their "risk-neutral probabilities" - in other words, he thinks they are letting some of their risk aversion creep into their statements about their beliefs. If that's true, then these surveys wouldn't be good evidence of behavioral craziness.

So the issue has not been decided yet. But progress has been made. In my opinion, the available evidence is suggestive of the "behavioral craziness" explanation, but not conclusive. The important thing is that this is not one of those "this will never be resolved" sorts of debates. This is a debate that can and will be resolved, as better and better data becomes available. Science progresses.

(Note: This blog post was edited to remove a term that I found out is actually a slur in the UK. No offense was intended.)

TLDR: Americans use spaz to mean a clumsy or over-excitable person while in British usage it's an offensive pejorative for a developmentally disabled person, approximately synonymous with retard. The American usage predates the British by at least 20 years.

I understand that "usefulness" plays a role here. I get that. If you can't build a model that allows you to predict particular outcomes within a useful range of uncertainty, then how will you predict the weather, right?

But useful weather models, IMO, only have to model some less arbitrary feedbacks (non-behavioral), and that's where I suspect DSGE-type models have a little trouble. I only suspect it (it's a hunch); I don't have a micro-founded model. LOL.

Barometric pressure, water temps, wind speeds, land surface temps, upper atmosphere temps and so on are fairly quantifiable, and yet local weather models that are used to predict things like tornadoes, hurricane landfall, and rainfall get into real trouble more than a few days in advance (they start becoming useless).

To me, and I could be wrong, it seems intuitive that Economic micro-founded models that attempt to predict "the local weather" would run into similar problems, but ... they would have the additional complication of attempting to quantify behavior that is often really not rational at all.

It's easier to extrapolate general trends (e.g. Global Warming due to greenhouse gas emissions), than it is to predict with any certainty what is going to be happening at any particular moment some place in particular :)

Not that people shouldn't try, and not that there aren't benefits to trying. Hurricane landfall and storm surge predictions have become a lot more useful in recent decades, for example. So there are possible benefits to micro-founded models.

But... call me crazy... I don't think I'll plan my wardrobe based on what somebody's micro-founded model says about the local weather 2 months from now.

Sorry to keep harping on this, but what about Steve Ross's paper "The Recovery Theorem", which shows how to infer the real-world measure from the risk-neutral measure using option prices? (Ross explicitly observes that knowing the real-world measure would allow estimation of the historical variability of the risk premium and thus "limit how predictable a model for returns could be and still not violate efficient markets."

Ross's sufficient conditions were pretty restrictive but Carr and Yu were able to relax them and still get some results, depending on the model chosen for the asset process, e.g. no recovery under Black-Scholes, but success under CIR. Since nobody believes that B-S is literally true anyway, that is not necessarily a fatal blow. But last I checked, they weren't able to derive general conditions under which recovery would work. So there is maybe scope for a research project / thesis there.

Hi Noah,You agree that 'Shiller would give a more rigorous definition of "bubble"'. Really? Well, if we macroeconomists can not tell the difference between a bubble and a fundamental rise in stocks (hint: if the Dow grows 5 times faster than nominal gdp, something is gonna explode), then we are useless. The society must stop wasting money on us. Let's face it.

What's wrong with the following definition? An asset price which has moved so far out of synch with any plausible fundamentals that it is bound to end badly for a great number of the people who bought said asset...

I'm not so sure about that. For example, Dean Baker detected the housing bubble in real time. He pointed out e.g. the huge deviation from historical norms in the ratio of housing and rental prices. He was certainly right, and I don't believe he had any general definition of bubble from which he was working. He just said something like "whatever a bubble is, this is a bubble."

If we forget about grad students and look at real traders in real markets and also forget about the small-time individual investor, (who doesn't count for much), then what we see are some diligent fundamentalists and a legion of technical traders who trade a lot more frequently than the fundamentalists and whose volume dominates on any given day. These are the main extrapolators. How prone are these guys to "behavioral craziness"? If you ask them they will say "not at all". Impulse trading is for losers, (like the small investor or the occasional grad student), and they adhere to technical systems specifically designed to prevent emotional trading. These systems, while mathematically sophisticated, produce predictions remarkably close to simple extrapolation in most cases.

There is this somewhat silly tension between "rational" and "behavioral" that can be resolved if we just acknowledge that traders AND economists have imperfect knowledge (that is why it is so hard to define a bubble ex ante). Traders realize that when asset prices are high relative to some benchmark value (think Price to Earnings), there is more risk of a reversal over the longer run. Twenty years is not the trading horizon of most traders though, and no one knows when the reversal is going to occur though (or if instead earnings will grow sufficiently to lower the PE ratio to sustainable levels), so if they expect high enough short term returns they may be willing to continue bidding the price up (the high expected return compensates for the risk associated with the high PE ratio, you could think about this in terms of the mean and skew to the distribution). No one can say what individuals should expect prices to do in the short term, the future is too novel, and what happens depends on expectations so it is indeterminate. Once we acknowledge this imperfect knowledge and short term horizons, behavioral heuristics (for example extrapolation) are not irrational. With that said, the survey evidence suggests the risk premium is pro-cyclical with the asset price, which is the opposite of the behavior Cochrane predicts, so he is off track.

To be fair to Cochrane, he cant just go out and slam his father in law and the creator of his career. Just think Noah, if you married well youd be part of the fresh water nobility too instead of kicking it out in the provinces.

"But others - such as Gene Fama - interpret long-run predictability as being due to predictable, slow swings in risk premia."

This doesn't seem right to me. Any predictability, or mean reversion, seems to violate market efficiency, no matter what the reason for it.

If the current public all has a risk premium of 2, and so the current stock prices reflect that, but everyone being a perfectly foresighted, perfectly optimizing cyborg knows that in 10 years the market risk premium is going to be 8, then they'd jump all over that now and push the current stock prices high enough now that they won't mean revert in the future.

Seems wrong what this quote is saying, but I'd have to see the exact details and explanation and models (if any).

Noah, both Shiller and Fama represent purist positions of some kind which may be natural for people who try to develop new paradigms/big ideas. To use terminology which has become popular of late (look up Phillip Tetlock if not familar), they both sound like big hedgehogs rather than foxes. So they're not good at presenting more balanced viewpoints(Lars Hansen is much bettter in this regard).

Efficient Markets Hypothesis is really just an early version of Rational Expectations and it suffers from similar benefits and flaws as a framework for thinking about the world. It allows you to take into account the pervasive impact of expectations on behaviour and get a 1st pass at an endogenous theory of how future expectations affect decisions today. It also forces you to think of other factors besides just saying people must be crazy when they don't think like you. This doesn't have to be about preferences like in habit formation models. The most promising explanations of financial prices using RE models are those incorporating heterogenous agents, incomplete financial markets, uninsured personal risks etc...look up research by people like Michalides and Gomes. This research basicallytries to explain time varying discount factors as emerging from aggregation over many investors with different sensitivity to aggregate risks. The costs of a pure RE/EMH approach is that it's unlikely to provide complete explanations. At which, point we can explain the residuals from the RE/EMH models using correlated expectational errors (Hersh Sheffrin has a good formalisation of this, and Hansen's nobel lecture as well). So realistically, you can't just say it's behavioural craziness, or it's rational risk premia. It's a mixture of both and I at least learn something from both types of models (and in macro and finance there is no choice but to always mentally mix stories and models at some point when analysing reality. Yes, there will never be a model of everything).

"But six undergrads trading tens of dollars in a computer lab is hardly a perfect proxy for the U.S. stock market, so the experimental evidence is suggestive rather than decisive."

I like that word "suggestive." I saw a dog acting funny yesterday, which suggested to me that all humans are crazy. You have to be more precise about this. What exactly is this craziness theory? What does it imply about what we should see in the data?

Actually, what I'm thinking is that there are no implications at all. Craziness, as Shiller seems to think about it, is just reflected in the difference between the data and what the best models we have predict. So, we could just call that ignorance. The housing "bubble" was driven by something we are ignorant of. In human behavior, craziness is another word for mental illness. But mentally ill people actually behave in very predictable ways, once your veil of ignorance is lifted.

I saw a dog acting funny yesterday, which suggested to me that all humans are crazy.

You should know that the original Vernon Smith bubble result has been replicated with professional trader participants and with much larger numbers of participants. Still suggestive rather than decisive, but more suggestive than just the original 6-undergrads-in-a-lab thing. Also, the original Smith experiment has been replicated hundreds of times (I have replicated it four times myself), so you should change your straw man from "I saw a dog acting funny" to "I always see dogs acting funny".

What exactly is this craziness theory?

P>FV

What does it imply about what we should see in the data?

P>E[FV|observables]

Actually, what I'm thinking is that there are no implications at all.

That's a perfectly logical way to think, given the paradox of induction.

In human behavior, craziness is another word for mental illness. But mentally ill people actually behave in very predictable ways, once your veil of ignorance is lifted.

This is a good point, and the reason I used the word "craziness" is because I had initially used the word "spazzing", but found out that this is a fairly serious slur in the UK. So I changed it. What I really mean is "suboptimal behavior coordinated across individuals". But that doesn't sound as cute.

1. I think what you're saying is that the Vernon Smith bubble experiment has been repeated many times with different subjects, and the experimenters get roughly the same results. So, the experimental subjects behave in predictable ways. They're not crazy at all.

2. Suppose that we could rerun the last 15 years with the same time series of "fundamentals" (you get to choose what those are). Does craziness theory tell us that we should observe the same time series of asset prices the second time around, or something different?

3. I assume that FV is financespeak for "fundamental value." I (and other people) have written down models which determine asset prices. If Shiller lived in those models, and measured P and FV, he would find P > FV. And the other people who live in that model are all hyper-rational.

Now we're getting to it. That's suboptimal given some objective function and some constraints. Maybe you just have the objective function or the constraints wrong.

That's always true. Objective functions will always be a free parameter. You can only restrict further and further the set of objective functions consistent with observed actions.

By the way, what do you mean by decisive?

I mean, something that would convince Noah Smith that real-world bubbles (of the "price goes up and then down") variety are often the result of investor mistakes rather than changes in discount rates.

http://www.lhup.edu/~DSIMANEK/cargocul.htm

I feel like I've made this joke before, only not about experimental economics... ;-)

So, the experimental subjects behave in predictable ways. They're not crazy at all.

Predictable in a lab doesn't mean predictable in the real world, even if the behaviors are one and the same in both domains. For example, suppose I find that in the lab, when I induce bad weather conditions, people predictably sell stocks. That doesn't mean that bad weather is predictable in the real world. See?

This also addresses Point #2.

I (and other people) have written down models which determine asset prices. If Shiller lived in those models, and measured P and FV, he would find P > FV. And the other people who live in that model are all hyper-rational.

Sure, investor irrationality is only one possible reason for P>FV in the real world. In the lab, the causes of P>FV can be (to some degree, hopefully to a large degree) controlled and separated.

"I saw a dog acting funny yesterday, which suggested to me that all humans are crazy."

Oy, com'on Stephen. Are you actually that detached from the real world that you think this kind of behavior and ginormous lack of expertise and knowledge is some rare crazy dog phenomenon. Well, here's some empirical data that's not crazy dog, it's percentages like 2/3rds:

• Suppose you had $100 in a savings account and the interest rate was 2 percent a year. After five years, how much do you think you would have if you left the money to grow? More than $102, exactly $102 or less than $102?

• Imagine that the interest rate on your savings account was 1 percent a year and that inflation was 2 percent. After one year, would you be able to buy more than, the same as or less than you could today with the money?

• Do you think this statement is true or false: “Buying a single company stock usually provides a safer return than a stock mutual fund”?

Anyone with even a basic understanding of compound interest, inflation and diversification should know that the answers to these questions are “more than,” “less than” and “false.” Yet in a survey of Americans over age 50 conducted by the economists Annamaria Lusardi of George Washington University and Olivia S. Mitchell of the Wharton School of the University of Pennsylvania, only a third could answer all three questions correctly.

Also, I don't know how you're defining P and FV, but as I remember it, If P>FV for an asset, then you could not buy it and get different assets instead that would give you the same risk-adjusted expected return at a lower price. And, if that's the case, "hyper-rational people would not pay that P, and it would fall if everyone was hyperrational. So I don't know how you're defining fundamental value.

Decisive: I was told in my first econometrics class that we can reject but we never accept. Science is never done.

You seem to want to take these lab experiments very seriously. In the experiments I have seen written up, I'm never much surprised by the results. Basically a group of undergraduates trying to figure something out. And you can't control what baggage the subjects bring into the experiment. A lot of people do this stuff now, but I think you have a lot of convincing to do with the rest of the economics profession.

Decisive: I was told in my first econometrics class that we can reject but we never accept. Science is never done.

That has always been my understanding as well.

You seem to want to take these lab experiments very seriously. In the experiments I have seen written up, I'm never much surprised by the results. Basically a group of undergraduates trying to figure something out.

Actually, in some recent experiments (including one of mine), people are finding that even when the subjects provably understand how the thing works, they act very weird unless we find some way to make them believe that the *other* subjects understand it too.

nd you can't control what baggage the subjects bring into the experiment. A lot of people do this stuff now, but I think you have a lot of convincing to do with the rest of the economics profession.

That is certainly true! I've been thinking of ways to do that.

Have you read David Levine's survey of experiments? He didn't say it explicitly, but I think the upshot is that when things are either static or non-stochastic, standard micro theories tend to do a good job of predicting lab results, but when things get dynamic+stochastic, we just don't understand much of what we see in the lab.

Then there's the problem of where all this leads. Some policymaker gets it in his or her head that people are acting crazy, and then starts trying to make them behave.

Well, maybe. But given the way policymakers behave in real life, I'd say heeding economics experiments is the least of their sins...

Anyway, I think the main implication of "inefficient markets" is in corporate finance. I strongly suspect that compensating executives with options and stock is a much worse idea than we think.

"but when things get dynamic+stochastic, we just don't understand much of what we see in the lab."

Some people have done monetary experiments, for example Gabriele Camera works on this. Those experiments are particularly difficult. In monetary models, there's typically in infinite horizon, and valued money is supported by the belief that people will accept the money in the future, which is supported by the belief that people in the future will accept money in the further future, etc. But how do you set that up in the lab? Some experimental designs have the experiment proceed in rounds, and we determine whether we proceed to the next round by rolling a die - so play stops with probability 1/6. So that might seem OK, as it seems there is always positive probability of going to the next round. But the players know that, when 5 pm comes, they are going to go home no matter what. When the subjects play the game, they typically trade the money - the stuff has value even though its "fundamental value" is zero. But note that, the way the experiment was set up, they're already violating the theory, as it's a finite game they're playing. I think they're valuing the money because they come into the experiment knowing what money is from their daily lives. They see some objects in the experiment and think, "this is money," and then they trade the stuff.

Yes, that's also how I've simulated an infinite horizon. When you get only a 0.001% chance of the experiment going past 5:00, I think you probably get pretty close to true infinite-horizon behavior, in terms of infinite # of periods. But of course, infinitely many periods and infinitely long time aren't the same thing, and you can't do an experiment where the results will affect a subject's entire future lifetime, so life-cycle effects are one thing that experiments will probably never have much to say about.

Sorry, Stephen, but the experimental evidence has been around since 1988 with the Vernon Smith et al paper in Econometrica and is a robust result reproduced in many setttings multiple times over, including in field experiments, not just labs with undergrads. People trading in finite discrete time with absolutely known payoffs at the end tend to bubble in the middle of the period before reverting to the fundamental at the end. It is true that this can be made to go away by having the same group do the same experiment over and over, but that is not what we see in the real world, where there is constant turnover of traders and newbies entering who have not yet learned.

The definition of a bubble is straightforward, but identifying them is hard. They are sustained movements away from fundamentals, but the problem is always observing that fundamental. While in many markets one can wave one's hands about "misspecified fundamentals," there are ones where one cannot do so. The most famous is closed-end fund markets, where the fundamenal is the net asset value of the fund minus some transactions costs and tax effects, which is why most such funds price at singe-digit discounts (I could cite a paper of mine on this, but won't). As it is Barsky and DeLong had a nice paper in the Journal of Economic History where they observed that closed-end funds soared to 100% premia in 1929, and concluded that "we cannot prove that the stock market was a bubble in 1929, but we are near certain that the closed-end fund market was," (or words to that effect).

As for using surveys to separate expectations from time-varying riks premia, this has been done for a long time,with a a paper by MacDonald and Torrance in 1988 in the Oxford Bulletin of Economics and Statistics being an early example on forex markets. And, yes, their evidence is that risk premia just do not vary all that much over time, so to ignore this one has to fall back on some such nonsense as declaring that people either knowingly or unconsciously misrepresent the truth in surveys.

I guess the bottom line for me is that I haven't seen experimental work or survey evidence that has changed my views about how the world works, or about how to do research. Experimental work is fraught with problems, and I already know that the actual behavior of any individual economic actor - me, for example - will look nothing like what I write down in models. I think learning on the part of market participants is probably important, but I also think that the learning models that people write down are pretty crappy. Solving learning models in a sensible way seems beyond what we know how to do technically. So, when I'm choosing how to do research, I tend to focus on the things that are feasible, and try to build on what we know well.

Thought I was done, but not yet. Here's an idea. It's not a craziness theory, but along the lines you're thinking about. It seems we have evolved to be optimistic and to think well of ourselves. If we took a poll, I think we would find (Lake Wobegon fashion) that the average person thinks they are well above average. That has served us well as a species - we survive, we prosper, we innovate. So, if we put these average people in a Vernon Smith experiment, they tend to be willing to accept an asset in exchange at a price higher than the fundamental, because they think there is some other dummy in the crowd who will take it at a higher price. I don't know what has already been done on this, but the theory project would be to put all of that in a model, and see what you need to make it fly. You want some initial evolution stage where the survivors tend to be the ones who think well of themselves, and then a stage where the survivors trade assets.

I think you are on the money with the Lake Wobegon effect argument. People start bubbling because they think they are smarter than the others and can make money by selling high and getting out before the others. Something like that. When it is repeated a bunch of times with the same group, they figure out that they cannot do so, at least not systematically.

What happens in the (financial) asset markets, is roughly something like this: an influential investor (think of a fund leveraging $15b+, not just one or two) spots the potential to start a price run. He goes on TeeVee. at that point, as a trader you either decide to go along with him or stay out. Other large fund managers decide to back the momentum and we have the beginnings of a "bubble". If you can exit with the big group (not necessarily telegraphed in real time), you win.

Actually there are quite a few studies that get directly at whether or not risk premia vary over time. The best are panel studies following groups of people to see what they do, especially with portfolio allocation. One such from 2006 is at www.columbia.edu/~pc2167/ChiapporiPaiellaOct2006.pdf . They find no evidence of any noticeable change in relative risk aversion for people in their sample panel, and this is consistent with pretty much every other study that has attempted to study how peoples' attitudes to risk change over time. They don't very much, certainly not remotely enough to support the Fama/Cochrane fantasy, and this has been in the lit for decades now, only getting more strongly supported and refined as we go along. One does not need to wave hands about people completely rewiring their brains. The data is there and pretty darned robust. This ballgame is basically over for anybody willing to look at the careful studies, not all of them just surveys but ones based on behavior as well.

"Decisive: I was told in my first econometrics class that we can reject but we never accept. Science is never done.

That has always been my understanding as well."

You're both bloody crazy. In the first place, I can accept anything I want to. The question is when SHOULD I accept. That's basically trivial.

But in the real world, as opposed to the fantasyland you two evidently inhabit, actual decisions need to be made. You can't just say "we're never done;" you have to actually do something. The something might be to determine what line of research to pursue, or whether to buy insurance personally, or whether society should collectively buy insurance against Global Warming.

So, hypotheses need to be accepted, even granting that we might need to change them in the future.

All of which was pointed out in 1954 by Richard Rudner in a paper published in Philosophy of Science titled "The Scientist Qua Scientist Makes Value Judgements."

And while we're on the subject of Richards, I can't resist pointing out the Feynman's understanding of the real Cargo Cultists, as opposed to his straw men, was essentially nonexistent. Anthropology was not his strong suit. Nor was philosophy, albeit the advice to bend over backwards to be completely honest is excellent. His undoubted genius didn't make him infallible (not even in physics; he made some famous blunders.)

"I think we would find (Lake Wobegon fashion) that the average person thinks they are well above average."

You THINK!? You're talking about this in ignorance of the decades of experimental results on the subject? The results of which were that yes people do think that, just in case you want to know.